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C₂×#22899 #6381483

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

(1,2);(3,4,8,13,10,14,9,12)(5,15,17,18,7,6,16,11);(3,5,8,17,10,7,9,16)(4,11,13,15,14,18,12,6);(3,6)(4,5)(7,14)(8,11)(9,18)(10,15)(12,16)(13,17);(3,7)(4,6)(5,10)(8,16)(9,17)(11,13)(12,18)(14,15)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6288679);